This paper is concerned with the construction and study of specific finite and infinite integral transforms arising from a singular Sturm-Liouville problem on a half line, which is connected to the hydrogen atom equation. The paper goes further to describe fully the image of some spaces of square integrable functions with respect to some measure under the finite and infinite integral transforms...

In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra  integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two ben...

In this paper we continue our investigations of square function inequalities in harmonic analysis. Here we investigate oscillation and variation inequalities for singular integral operators in dimensions d ≥ 1. Our estimates give quantitative information on the speed of convergence of truncations of a singular integral operator, including upcrossing and λ jump inequalities.

The computation schemes of spline-collocation methods for solving singular integral equations. A theoretical foundation of these two methods is obtained in space L2. In the present paper we give theoreticaly justification of the numerical schemes of spline-collocation method for solving the singular integral equations (SIE) of the following form

Weighted norm inequalities are proved for a rough homogeneous singular integral operator and its corresponding maximal truncated singular operator. Our results are essential improvements as well as extensions of some known results on the weighted boundedness of singular integrals.

The asymptotic behavior of the singular and entropy numbers is established for the Erdelyi–Köber and Hadamard integral operators (see, e.g., [15]) acting in weighted L spaces. In some cases singular value decompositions are obtained as well for these integral transforms. 2000 Mathematics Subject Classification: 47B06, 47B34, 47H50.